Pay Your Bills or Lose Your Pay Act of 2013 - Requires the appropriate payroll administrator of each house of Congress to deposit in an escrow account all mandatory payments for compensation of Members of Congress serving in that house during a specified period beginning when the federal government is unable to make payments or meet obligations because the public debt has been reached. Requires release of such payments to those Members only upon the earlier of: (1) the date on which both chambers present a bill to the President to increase the public debt, or (2) the last day of the 113th Congress.